A Study On The Teaching Cases Of Tacit Knowledge In High School Mathematics

At present,high school mathematics education is in the stage of inheriting the new and old curriculum standards,the cultivation stage of mathematics core accomplishment and the integration stage of advocating mathematics culture and mathematics classroom.Many high school mathematics teachers,especially novice mathematics teachers,often feel unable to grasp the contents and methods of mathematics teaching in this transitional stage.Learning the essence of mathematics is the key and essence of mathematics learning.The essence of mathematics is often some "tacit knowledge" which can only be understood and can not be expressed by words,such as exponential thinking method.In the process of learning mathematics essence,often need to use mathematical culture such as the carrier,in the understanding of knowledge in the process of the occurrence,development and the cultivation of the core of mathematics literacy also played a positive role,therefore,in mathematics learning is very necessary to properly "tacit knowledge" mining and infiltration.Based on the existing research of explicit tacit knowledge theory,this paper combines the relevant theories of tacit knowledge with the teaching and learning of mathematics by combining the object of mathematics with the abstract and formal materials.Combining the experience of expert teachers and novice teachers,this paper expounds the necessity of exploring and penetrating "tacit knowledge" in mathematics teaching and learning in senior high school from three aspects: mathematics curriculum standards,teachers and students.By comparing the characteristics of tacit knowledge that can only be understood and cannot be expressed in words,and combining with the mathematics teaching materials in high school,the author puts forward the "semi-tacit knowledge"--the mathematics and the knowledge directly related to mathematics that students must master in the whole process of mathematics learning in order to better understand the contents of the teaching materials,which is not mentioned in the teaching materials.Through to the high school mathematics learning of "tacit knowledge" and "tacit knowledge" of digging,to some extent compensate for the teaching material of "holes".And from two aspects: teachers and students of high school mathematical teaching and learning in the mining and penetration "tacit knowledge" and "tacit knowledge" of the strategy and method,according to the high school mathematics knowledge of two parts--mathematics concept and mathematics proposition,in specific cases appropriate USES "textbook reconstruction","mathematics teaching under the perspective of HPM",of "knowledge directly added," the way in which contain the "tacit knowledge" and "tacit knowledge" of penetration.On the one hand,it provides a reference for teachers' teaching;on the other hand,it helps students better grasp the essence of mathematics and improve their mathematical literacy.